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If two 6-digit numbers 18196x and 2321y8 are exactly divisible by 24. What will be the remainder when a three-digit number x1y is divided by 11?

If two 6-digit numbers 18196x and 2321y8 are exactly divisible by 24. What will be the remainder when a three-digit number x1y is divided by 11? Correct Answer 9

If a number is divisible by 24, then the number must be divisible by both 3 and 8.

From the condition of divisibility by 8 we know,

96x must be divisible by 8.

So, x must be equal to 0 or 8, however by checking divisibility by 3, x will be 8.

Now from the condition of divisibility by 3 we know,

(2 + 3 + 2 + 1 + y + 8) = (16 + y) must be divisible by 3

So Possible value of y are 2, 5, 8

But 1y8 also must be divisible by 8

So, desired value of y = 2.

So required number = x1y = 812

So, remainder of 812/11 = 9

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